Before boring yourself by reading the docs in detail, you can dive right into tsfresh with the following example:

We are given a data set containing robot failures as discussed in [1].
Each robot records time series from six different sensors.
For each sample denoted by a different id we are going to classify if the robot reports a failure or not.
From a machine learning point of view, our goal is to classify each group of time series.

You end up with a DataFrame extracted_features with all more than 1200 different extracted features.
We will now remove all NaN values (that were created by feature calculators, than can not be used on the given
data, e.g. because it has too low statistics) and select only the relevant features next:

You can now use the features contained in the DataFrame features_filtered (which is equal to
features_filtered_direct) in conjunction with y to train your classification model.
Please see the robot_failure_example.ipynb Jupyter Notebook in the folder named notebook for this.
In this notebook a RandomForestClassifier is trained on the extracted features.